It works fine, my own setup is different machines like yours.
To troubleshoot compare the entity id of the camera with the frigate config. Are they identical?
Is mqtt working? Can you see mqtt messages
of events making it to home assistant? Check mqtt logs.
Check home assistant logs for errors.
You need to create another group, you can have device groups, people groups etc just needs to only be entities that have the home or not home states. Then use this entity for that field.